It may be tempting fate to try to gather 60 heads of state and hundreds of global business leaders in the dead of winter in a Swiss mountain valley. This year, the World Economic Forum's luck seems to have run out.

Fat, damp snowflakes have been tumbling down for the past six days, burying the town in six feet of snow, three feet of it in the last two days alone. Snow was still falling fast on Monday night, and the steep, pine-dotted slopes were so heavily laden that some neighborhoods here in Davos had to be evacuated for fear of avalanches.

Head-high snow drifts quickly piled up along the roads, leaving no place for street plows to push more snow. Sidewalks completely disappeared. Pedestrians slipped and slid in traffic between huge trucks and luxury minivans on streets carpeted with compacted ice several inches thick.

Davos is not alone in getting clobbered with snow in Switzerland this winter. Just two weeks ago, 13,000 tourists were stranded at the foot of the Matterhorn by heavy snow and rain. But the timing of the snowfall — on the eve of the World Economic Forum's annual conference — has had an outsize impact.

By Sunday night, heavy snow had already blocked the rail line through the Alps from Zurich, and villages along the route were at the highest level of avalanche alert. Swiss Rail began unloading Davos-bound passengers from their express trains, taking them on a half-hour bus trip on back roads around the blockage and then loading them onto a crowded red commuter train that ran the rest of the way into Davos.

"What shall we do," the mayor of Davos, Tarzisius Caviezel, said at a news conference on Monday, admitting he was at a loss for how to respond. "It's impossible."

There was too much snow to find places to put in the narrow, steep-sloped valley, he explained, and no easy way to take it anywhere else. That throngs of uber-wealthy conference goers and their entourages were trying to push their way toward Davos did not help. A giant purple freight truck wound up in a snow bank on Monday morning across the street from the conference center, temporarily paralyzing the already slow-moving traffic.

"We can do nothing," Mr. Caviezel said, except wait for better weather to arrive, perhaps some time on Tuesday, and gradually dig out.

The mayor had been expected to be joined at the news conference by Ulrich Spiesshofer, the chief executive of ABB, the Zurich-based multinational. ABB makes some of the world's brawniest electrical power equipment for the world's harshest and most remote locations. But Mr. Spiesshofer arrived late because his car was stuck in traffic.

In perhaps the most harrowing indignity for the plutocrats who have made the World Economic Forum their favorite winter meeting ground, even the town's helicopter pad was closed because of the snowstorm. By early afternoon, a quarter-mile trip in one of the ubiquitous black luxury minivans with plush leather seats that shuttle participants around the town took nearly an hour.

Linda P. Fried, the dean of Columbia University's Mailman School of Public Health, allowed three hours at midday on Monday to travel from her hotel to the uncrowded registration center nearby and then a few blocks to the conference. But because of the gridlock, she was a half-hour late to give her speech. The topic had been the health risks that arise from climate change.

"I've been coming for eight years and this is the worst I've seen it," she said. But she bristled when asked whether some — like perhaps President Trump — might question the incongruity of discussing global warming during a blizzard.

"It isn't accurate, people just don't understand, that's not the metric," she said.

Climate scientists have long warned that rising emissions of greenhouse gases by humanity may cause weather extremes, and not just heat waves. But it is hard to link any single weather event to climate change.

Still, there were some who liked the snow: avid skiers.

"I skied here as a kid," said Anthony Couse, the chief executive for Asia at Jones Lang LaSalle Property Consultants, "and there definitely was not this much snow."